If `(x)/(x-1)+(x-1)/(x)>0` then x is

If f(x)=(x-1)/(x+1),x!=-1, then show that f(f(x))=-1/x provided that x != 0,-1

If f(x)=(x-1)/(x+1),x!=-1, then show that f(f(x))=-1/x provided that x!=0,1.

If f(x)= |1 x x+1 2x x(x-1)(x+1)x3x(x-1)x(x-1)(x-2)(x+1)x(x-1)| then f(500) is equal to a. 0 b. 1 c. 500 d. -500

If f(x)=|(1, x, x+1), (2x, x(x-1), (x+1)x), (3x(x-1), x(x-1)(x-2), (x+1)x(x-1))| then f(5000) is equal to 0 b. 1 c. 500 d. -500

If f(x)=|\(1,x,x+1),(2x,x(x-1),(x+1)x,3x(x-1),x(x-1)(x-2),(x+1)x(x-1))| then f(100) is equal to (A) 0 (B) 1 (C) 100 (D) -100

If f(x)=|(1,x,x+1),(2x,x(x-1),(x+1)x),(3x(x-1),x(x-1)(x-2),(x+1)x(x-1))|, then f(100) is equal to - (i) 0 (ii) 1 (iii) 100 (iv) -100

If f(x)=(x-1)/(x+1),x!=-1, . then show that f(f(x))=-1/x , prove that x!=0 .

If f(x) = (1)/(1 -x) x ne 1 and g(x) = (x-1)/(x) , x ne0 , then the value of g[f(x)] is :

If tan ^(-1) ((1-x)/(1+x))= (1)/(2) tan^(-1) x, x gt 0 , then x = ?

If f(x)={:{(xe^(-(1/(|x|) + 1/x)), x ne 0),(0 , x =0 ):} then f(x) is